Approximation Of Model Research Articles

Dual symmetries of dense isotopically and chirally asymmetric QCD

In the present paper, the dual symmetries of dense quark matter phase diagram found in some massless three- and two-color NJL models in the mean field approximation have been shown to exist at a more fundamental level as dual transformations of fields and chemical potentials leaving the Lagrangian invariant. As a result, the corresponding dual symmetries of the full phase diagram can be shown without any approximation. And it has been shown not only in the NJL models, but also in framework of two- and three-color massless QCD itself. This is quite interesting, since one might say that it is not very common to show something completely non-perturbatively in QCD.

π-π scattering lengths: Electric corrections in the linear sigma model

In the frame of the linear sigma model and working in the weak field approximation, we discuss the role played by an external electric field on the behavior of π-π scattering lengths. For this purpose, we have considered all relevant one-loop diagrams in the s, t, and u channels where we have Schwinger propagators for charged pions. An important novelty of our analysis, compared with previous existing discussions in the literature, is the explicit calculation of box diagrams which were previously not considered in discussions regarding magnetic corrections to π-π scattering lengths. Our analysis shows that electric field corrections have an opposite effect with respect to the previously calculated magnetic corrections.

New slow-roll approximations for inflation in Einstein-Gauss-Bonnet gravity

We propose new slow-roll approximations for inflationary models with the Gauss-Bonnet term. We find more accurate expressions of the standard slow-roll parameters as functions of the scalar field. To check the accuracy of approximations considered we construct inflationary models with quadratic and quartic monomial potentials and the Gauss-Bonnet term. Numerical analysis of these models indicates that the proposed inflationary scenarios do not contradict to the observation data. New slow-roll approximations show that the constructed inflationary models are in agreement with the observation data, whereas one does not get allowed observational parameters at the same values of parameters of the constructed models in the standard slow-roll approximation.

Specific line shape of the lowest frequency Raman scattering modes of triethylene glycol.

For both dielectric spectroscopy and light scattering spectra, the relaxation modes in the microwave region have been characterized by the Debye relaxation model, which is determined by the peak frequency, or by an empirically extended model (e.g., Cole-Davidson and Kohlrausch-Williams-Watts), which has the appropriate line shape. For light scattering from glass-forming liquids, the general line shape is a broader high frequency side in comparison with Debye relaxation. However, for triethylene glycol (TEG) in liquid form at room temperature, the lowest frequency Raman scattering (LFR) mode shows a peak at about 3.0GHz, which is narrower than that expected for the Debye relaxation. With increasing temperature, this peak exhibits a significant blueshift and begins to resemble the Debye relaxation shape, indicating that the LFR mode of TEG is also a relaxation mode. The narrowing of the LFR mode of TEG is suggested to be caused from the increased non-whiteness of the fluctuation correlations due to increased hydrogen bonding. This is a consequence of breaking the Debye relaxation model's approximation of the overdamping and narrowing limits in the GHz region, which was found in this study by analyzing the relaxation modes of Raman scattering using the multiple random telegraph model for evaluating thermal bath correlation. The analysis results show that the LFR relaxation times of TEG and the main dielectric relaxation overlap only by 333K. However, the second LFR mode and β-relaxation at higher frequencies coincide over a wide temperature range, suggesting that they are corresponding modes.

Anatomy of critical fluctuations in hadronic matter

Critical phenomena in phase transitions of strongly interacting matter, governed by quantum chromodynamics, are inherently encoded in the fluctuations of conserved charges. In this work, we study the net-baryon number density fluctuations, including the lowest-lying nucleon and the baryonic resonance Δ(1232), based on the parity doublet model in the mean-field approximation. We focus on the qualitative features of the second-order susceptibility of the net-baryon number density in dense hadronic matter and how the inclusion of Δ(1232) affects it. We demonstrate that the fluctuations of the individual baryons do not necessarily reflect the total net-baryon number fluctuations at finite density, due to the nontrivial correlations between different particle species. Our results highlight the role of baryonic correlations in the interpretation of data from heavy ion collision experiments. Published by the American Physical Society 2024

Thermodynamic behavior of CrF2 corrosion product in the molten LiF-ThF4 salt system

This work examines the thermochemistry of the chromium difluoride CrF2 corrosion product in the molten ▪ fuel salt system. Through a combination of experimental investigations and thermodynamic modeling assessment, the study elucidates the thermodynamic properties, phase diagram equilibria, and overall thermodynamic behavior of CrF2 corrosion product, following dissolution from a structural material to the molten salt fuel environment. In this work, two different synthesis methods were developed for pure CrF2, further allowing to experimentally measure the phase equilibria in the ▪ , ▪ , and ▪ systems. Then, thermodynamic models were developed using the CALPHAD method based on the quasichemical model in the quadruplet approximation.

Fermionic condensate and the vacuum energy-momentum tensor for planar fermions in homogeneous electric and magnetic fields

We consider a massive fermionic quantum field localized on a plane in external constant and homogeneous electric and magnetic fields. The magnetic field is perpendicular to the plane and the electric field is parallel. The complete set of solutions to the Dirac equation is presented. As important physical characteristics of the vacuum state, the fermion condensate and the expectation value of the energy-momentum tensor are investigated. The renormalization is performed using the Hurwitz function. The results are compared with those previously studied in the case of zero electric field. We discuss the behavior of the vacuum expectation values in different regions for the values of the problem parameters. Applications of the results include the electronic subsystem of graphene sheet described by the Dirac model in the long-wavelength approximation.

Neural networks for turbulent transport prediction in a simplified model of tokamak plasmas

The method of using neural networks (NNs) for turbulent transport prediction in a simplified model of tokamak plasmas is explored. The NNs are trained on a database obtained via test-particle simulations of a transport model in the slab-geometrical approximation. It consists of a five-dimensional input of transport model parameters, and the radial diffusion coefficient as output. The NNs display fast and efficient convergence, a validation error below 2 % , and predictions in excellent agreement with the real data, obtained orders of magnitude faster than test-particle simulations. In comparison to a spline interpolation, the NN outperforms, exhibiting better predicting and extrapolating capabilities. We demonstrate the preciseness and efficiency of this method as a proof-of-concept, establishing a promising approach for future, more comprehensive research on the use of NNs for transport predictions in tokamak plasmas.

Laser-assisted (e,2e) study with twisted electron beam on H-atom

We study the laser-assisted twisted electron beam impact ionization of the hydrogen atom in coplanar asymmetric geometry. We develop the theoretical model in the first Born approximation. In the presence of the laser field, we treat the incident and scattered electrons as Volkov waves; the ejected electron, moving in the combined field of the laser and residual ion H+ , as a Coulomb–Volkov wave function. In this communication, we compare the angular profile of triple differential cross-section (TDCS) for laser-assisted twisted electron beam incidence with the plane-wave, laser-assisted plane wave, and field-free twisted electron beam for (e,2e) processes for different orbital angular momentum (OAM) number (ml ) values. We analyze the effect of impact-parameter b of twisted electron beam and the laser parameters on the angular distribution of the TDCS. We study the (TDCS)av for the macroscopic target to examine the effect of opening angle θ p of the twisted electron beam on the angular profile of TDCS. We also observe the influence of coherent superposition of two Bessel states on the angular profile of TDCS. Our results clearly show the effects of laser parameters (electric field ɛ and number of photon exchanged (l)) and twisted electron beam parameters (OAM number (ml ) and opening angle (θ p )) on the angular distribution of TDCS.

Local discontinuous Galerkin for the functional renormalisation group

We apply a Local Discontinuous Galerkin discretisation to flow equations of the O(N)-model in the Local Potential Approximation. The improved stability is directly observed by solving the flow equation for various N and space-time dimensions d. A particular focus of this work is the numerical discretisation and its implementation. It is realised as a module within the high performance PDE framework DUNE. A preliminary version of the module is available on GitHub, but it is not submitted for publication as it is too early to be archived.

The XYZ model in the mean-field approximation in terms of Pauli spin matrices

The mean-field approximation (MFA) of spin-1/2 XYZ model was studied by using the Pauli spin matrices and their exponentials which led to very nice hyperbolic tangent functions in nonlinear form. The magnetization components Mx, My and Mz were obtained for the ferromagnetic (FM) case and then it was modified for the antiferromagnetic (AFM) case by introducing the sublattices. The bilinear exchange interaction parameters Jx, Jy and Jz, and the external magnetic fields Hx, Hy and Hz were considered along the three-dimensions for various coordination numbers q = 3, 4 and 6. The thermal variations of the magnetizations and thus the phase diagrams were obtained to illustrate the behaviours of phase transition lines in the AFM case.

EVALUATION OF THE EFFICIENCY OF THE AUTOMATED ALGORITHM FOR DRAWING SHIP HULL SURFACES

The efficiency of application of the algorithm for automated construction of ship hull surfaces using NURBS approximation is shown. In the majority of modern shipbuilding CAD-systems a considerable share of labor intensity is occupied by preparation of the ship surface model in the first approximation on the basis of electronic theoretical drawing. For carrying out such works in shipbuilding CAD-systems there is a corresponding computer toolkit, which allows to display geometrically clear smooth forms of such surfaces as a ship hull. The works of domestic and foreign researchers in this field have been analyzed. The proposed solutions have significant disadvantages: they require large computing power for training and use. The paper shows a modern approach to solving the issue of reducing the labor intensity of graphical constructions and, consequently, time costs by automating the procedures of computer modeling using web technology. Computer modeling of bulbous bow ends and tunnel-type stern parts is a labor-intensive process of manual editing of hull geometry. Experimental studies of the developed automated algorithm and software product for this type of work have been carried out. The comparative analysis of labor intensity of construction of the most complex part of the ship surface – the bow tip of ships of three projects using the developed software product and two professional CAD-systems – KOMPAS-3D and Rhinoceros – is given. The comparison showed that the developed algorithm and program are much more efficient to use compared to the toolkit of the compared CAD systems. The automated algorithms developed in the process of research can be used in shipbuilding practice, ship repair tasks, as well as for hydrostatic calculation programs.

Inflation based on the Tsallis entropy

We study the inflationary scenario in the Tsallis entropy-based cosmology. The Friedmann equations in this setup can be derived by using the first law of thermodynamics. To derive the relations of the power spectra of the scalar and tensor perturbations in this setup, we reconstruct an f(R) gravity model which is thermodynamically equivalent to our model in the slow-roll approximation. In this way, we find the inflationary observables, including the scalar spectral index and the tensor-to-scalar ratio in our scenario. Then, we investigate two different potentials in our scenario, including the quadratic potential and the potential associated with the natural inflation in which the inflaton is an axion or a pseudo-Nambu–Goldstone boson. We examine their observational viability in light of the Planck 2018 CMB data. We show that although the results of these potentials are in tension with the observations in the standard inflationary setting, their consistency with the observations can be significantly improved within the setup of the Tsallis entropy-based inflation. Moreover, we place constraints on the parameters of the considered inflationary models by using the current observational data.

Dissociative electron attachment to carbon tetrachloride probed by velocity map imaging.

Bond-breaking in CCl4via dissociative electron attachment (DEA) has been studied using a velocity map imaging (VMI) spectrometer. A number of effects related to the dissociation dynamics have been revealed. The near-zero eV s-wave electron attachment, which leads to the production of Cl- anions, is accompanied by a very efficient intramolecular vibrational redistribution. This is manifested by a small fraction of the excess energy being released in the form of the fragments' translation energy. A similar effect is observed for higher-lying electronic resonances with one exception: the resonance centered around 6.2 eV leads to the production of fast Cl2- fragments and their angular distribution is forward peaking. This behavior could not be explained with a single-electronic-state model in the axial recoil approximation and is most probably caused by bending dynamics initiated by a Jahn-Teller distortion of the transient anion. The CCl2- fragment has a reverse backward-peaking angular distribution, suggesting the presence of a long-distance electron hopping mechanism between the fragments.

Plasma screening effect in warm solid-density iron plasma

We study a plasma screening effect in a warm solid-density iron plasma. All the calculations are done using the average atom model in the muffin-tin approximation using the density functional theory in local density approximation at finite temperature in local thermodynamic equilibrium. Between temperatures equal to 15 and 20 eV, the system undergoes a huge change due to the 3d orbital becoming bound. In clear, four electrons become bound. Various average ionizations are defined to see this effect. At temperature equal to 20 eV, all the average ionizations agree to predict a Fermi energy and a plasma frequency that are close to the temperature of the medium. The density of states show a prominent resonance due to d orbital just below temperature equal to 15 eV. We show that the spectral opacity is drastically modified near the L shell threshold due to the appearance of a 2p→3d absorption line.

Monitoring casing corrosion of legacy wells using CSEM: Implications for large-scale energy and CO2 storage projects in shut-down hydrocarbon fields

Large-scale CO2 and energy storage is a mandatory part of the green shift to reduce CO2 emissions and limit consequences of climate change. Large-scale storage will require the use of shut-down depleted hydrocarbon fields to take advantage of well-characterized reservoirs and cap rocks. Thanks to extensive data from historical hydrocarbon production, the uncertainties related to storage capacity, injectivity, and containment are limited. However, legacy exploration and production infrastructure, and especially legacy wells, are the main threat for possible fluid leakage toward the surface. Such legacy wells are numerous and penetrate the full rock column. In this paper, we describe a workflow to screen and monitor legacy wells in the shut-down Frigg Field in the North Sea. By using numerical modeling of electromagnetic (EM) field propagation in one of the Frigg Field wells, we explore the complex interactions of fields, currents, and well structure in the presence of corrosion. The corrosion is implemented as a change in the electrical conductivity of the innermost steel casing at different depths along the structure. To enhance probing depth, we plug the dipole source (1 km long) into the casing at the seafloor and excite the casing as an antenna. We find that at moderate levels of corrosion, the current distribution is significantly modified with respect to the uncorroded case. This generates a signal that propagates and can be observed at the seafloor in the numerical results. Other elements of the well geometry (e.g., concentric overlapping cement casings) have their own effect on the signal. This leads the possibility of estimating the location of the corroded area within the well geometry. These results suggest that by relaxing some of the model's approximations and implementing realistic transmitters, it will be possible to evaluate and optimize controlled-source EM survey strategies for detecting and monitoring corrosion levels.

Regular multi-horizon Lee-Wick black holes

In this paper we carry out a detailed analysis of the static spherically symmetric solutions of a sixth-derivative Lee-Wick gravity model in the effective delta source approximation. Previous studies of these solutions have only considered the particular case in which the real and the imaginary part of the Lee-Wick mass μ = a + ib are equal. However, as we show here, the solutions exhibit an interesting structure when the full parameter space is considered, owing to the oscillations of the metric that depend on the ratio b/a. Such oscillations can generate a rich structure of horizons, a sequence of mass gaps and the existence of multiple regimes for black hole sizes (horizon position gaps). In what concerns the thermodynamics of these objects, the oscillation of the Hawking temperature determines the presence of multiple mass scales for the remnants of the evaporation process and may permit the existence of cold black holes with zero Hawking temperature T and quasi-stable intermediate configurations with T ≈ 0 and a long evaporation lifetime. For the sake of generality, we consider two families of solutions, one with a trivial shift function and the other with a non-trivial one (dirty black hole). The latter solution has the advantage of reproducing the modified Newtonian-limit metric of Lee-Wick gravity for small and large values of r.

Thermodynamic Assessment of the NaCl-CrCl2, NaCl-CrCl3, and FeCl2-CrCl2 Pseudo-Binary Systems for Describing the Corrosion Chemistry Between Molten Salt Fuel and Steel

A thorough understanding of the corrosion chemistry between molten salt fuel and structural materials (e.g., steel) is key for the advancement of Molten Salt Reactor technology. In this work, we consider more specifically the case of a chloride fuel salt mixture and the thermochemistry of a salt mixture such as (NaCl-MgCl2-PuCl3) in interaction with (Fe, Cr, Ni). The present work aims at the development of a thermodynamic model of the key subsystems NaCl-CrCl2, NaCl-CrCl3, and FeCl2-CrCl2 to predict corrosion products that may form between molten salt and structural materials. The Modified Quasichemical Model in the quadruplet approximation is used to describe the Gibbs energy of the liquid phase. A critical review of the existing phase diagram and thermodynamic data on theses systems is first presented. To alleviate the lack of data, ab initio calculations coupled with a quasi-harmonic approach are performed to estimate the thermodynamic properties for the intermediate solid compounds Na2CrCl4 and Na3CrCl6, which exist in the NaCl-CrCl2 and NaCl-CrCl3 systems, respectively. These atomistic simulation data together with selected experimental data are then used as input for the thermodynamic assessment of the three subsystems.

Current-voltage characteristics of single-stage semiconductor magnetic pulse generators with a distinctive structure of the conversion link in the input circuit

Introduction. The main feature of the semiconductor magnetic pulse generators (SMPGs) is a slow accumulation of energy in the primary capacitor and its rapid introduction into the load by using a series of sequentially connected magnetic compression stages. Initially, these devices were mainly used for pumping gas lasers, but over the last decade SMPGs have been increasingly used in electric discharge technologies for water purification and air ionization to remove toxic impurities. At the same time, along with the practice of using these devices, development has also been achieved in the principles of their design and methods of mathematical modeling. Problem. The main drawback of the existing theory of SMPG’s stationary oscillations mode is an adoption of the saturable reactor (SR) model in approximation of the static magnetization curve of its core, as well as unidirectional nature of the energy transfer from the generator to the load. In most publication the exchange processes between the power source and SR are still not covered. Goal. Study of electrical and energy characteristics of low-voltage single-stage SMPG devices with series and parallel conversion stages in the charging circuit. Methodology. To achieve the set goal, this work uses comprehensive approach relayed on technical tools of setting up the experiment, numerical methods for processing measurement results, as well as an analytical method for describing electromagnetic processes in single-stage SMPG circuits. Results. The closed current-voltage characteristics of the SR are obtained, according to which the numerical calculations of the integral magnetic and energy characteristics of the proposed models are carried out. The features of the longitudinal capacitance charging process in a SMPG’s circuit with a parallel conversion stage, which occurs simultaneously in two adjacent circuits, are explained. Analytical expressions to describe the dynamics of magnetic flux density in the SR’s core as a time-depended function are derived. Based on the obtained hysteresis curve of the core, the exchange processes of energy transfer between the power source and the SR are explained. Practical value. The results of the research can be applied in the development of low-voltage SMPG circuits with improved energy-dynamic parameters.

Nudged Elastic Bands and Lightly Bound Skyrmions

It has become clear in recent years that the configuration space of the nuclear Skyrme model has, in each topological class, many almost degenerate local energy minima and that the number of such minima grows with the degree (or baryon number) $B$. Rigid body quantization, in which one quantizes motion on the spin-isospin orbit of just one minimum, is thus an ill-justified approximation. Instead, one should identify a (finite-dimensional) moduli space of configurations containing all local minima (for a given $B$) as well as fields interpolating smoothly between them. This paper proposes a systematic computational scheme for generating such a moduli space: one constructs an energy minimizing path between each pair of local minima, then defines the moduli space to be the union of spin-isospin orbits of points on the union of these curves, a principal bundle over a graph. The energy minimizing curves may be constructed in practice using the nudged elastic band method, a standard tool in mathematical chemistry for analyzing reaction paths and computing activation energies. To illustrate, we apply this scheme to the lightly bound Skyrme model in the point particle approximation, constructing the graphs for $5\leq B\leq 10$. We go on to complete the quantization for $B=7$, in which the graph has two vertices and a single edge. The low-lying quantum states with isospin $1/2$ do not strongly localize around either of the local energy minima (the vertices). Their energies rise monotonically with spin, conflicting with experimental data for Lithium-7.